Actually Daniel saw it differently also. So let's go back to Daniel 2:35:
Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshing floors; and the wind carried them away, that no place was found for them: and the Stone that smote the image became a great mountain, and filled the whole earth.
What is this metaphorical stone, and how did it become a great mountain filling the whole earth? It is quite clear that this verse is speaking about the destruction of all the kingdoms of the world, and the establishment of the Kingdom of God (the Great Mountain) on earth under Christ (who is the Stone, and the Rock). Babylon (gold) was succeeded by Medo-Persia (silver), which was succeeded by Greece (brass), which was succeeded by Rome (iron).
Clay (mixed with iron) represents the nations of the former Roman empire ( all the countries surrounding the Mediterranean). But the wind did not carry them away in the first century. The Roman and then the Byzantine empires remained on earth until the 15th century. And then the Holy Roman Empire remained until the 19th century.
However, Daniel saw Christ establishing His future Kingdom on earth (which includes the Millennium) as follows (Dan 7:13,14) and this will happen after the Second Coming of Christ: